However, it's not the actual song itself that's in the film. It's a cover version of the song, performed by John Mellencamp.
The scene you're remembering is when Forrest is sitting on the bench, reflecting on his life and the world around him, and "Blowin' in the Wind" plays in the background. It's a powerful moment in the film, and the song perfectly captures the sense of wonder and confusion that Forrest experiences.